Model predictive control is a strategy well-suited to handle the highly complex, nonlinear, uncertain, and constrained dynamics involved in aircraft engine control problems. However, it has thus far been infeasible to implement model predictive control in engine control applications, because of the combination of model complexity and the time allotted for the control update calculation. In this paper, a multiplexed implementation is proposed that dramatically reduces the computational burden of the quadratic programming optimization that must be solved online as part of the model-predictive-control algorithm. Actuator updates are calculated sequentially and cyclically in a multiplexed implementation, as opposed to the simultaneous optimization taking place in conventional model predictive control. Theoretical aspects are discussed based on a nominal model, and actual computational savings are demonstrated using a realistic commercial engine model.